Failure of solve.QP in portfolio modeling
One correction and another comment. I should have said that a trade optimizer not caring about positive definiteness is usually a bad thing -- it has its uses but giving the optimizer a shot at a portfolio with negative variance is asking for trouble (because it will do its best to get there). The estimates of the variance with only a few observations are going to be extremely noisy. I think the length of history to be used to estimate the variance should depend on what length gives the best variance estimate and should be independent of the rebalancing schedule. (Though perhaps I have misinterpreted the original post.) Pat
On 22/09/2015 19:59, Patrick Burns wrote:
You can use a factor model or shrinkage to get a positive definite variance matrix. There is a function for each in the BurStFin package on CRAN. The optimizer in Portfolio Probe doesn't care about positive definiteness (though that is not always a good thing). It is free for academic use. Pat On 22/09/2015 14:37, aschmid1 wrote:
Hi everyone, I'm trying to estimate optimal Markowitz portfolio weights for a list of stocks chosen upon some criterion using solve.QP from quadprog library. When the number of stocks N reaches some limit, I get a message "matrix D in quadratic function is not positive definite." For example, if I rebalance every 6 weeks (which implies that variance is calculated for 6-week interval prior to the period for which I calculate portfolio weights), I can get solution for 25>=N<50. For 12-week interval, solution exists for 50>=N<100, and for 24-week interval, I can get solution for N=100. My attempt to remedy this problem with Higham's method doesn't help. I'll greatly appreciate you input: first, why this may happen (can there be lack of local minimum?), and second, whether there are R solvers that may need only semi positive definite matrix. Thanks! Alec
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